22,585 research outputs found
Frobenius and the derived centers of algebraic theories
We show that the derived center of the category of simplicial algebras over
every algebraic theory is homotopically discrete, with the abelian monoid of
components isomorphic to the center of the category of discrete algebras. For
example, in the case of commutative algebras in characteristic , this center
is freely generated by Frobenius. Our proof involves the calculation of
homotopy coherent centers of categories of simplicial presheaves as well as of
Bousfield localizations. Numerous other classes of examples are discussed.Comment: 40 page
Convex Trace Functions on Quantum Channels and the Additivity Conjecture
We study a natural generalization of the additivity problem in quantum
information theory: given a pair of quantum channels, then what is the set of
convex trace functions that attain their maximum on unentangled inputs, if they
are applied to the corresponding output state?
We prove several results on the structure of the set of those convex
functions that are "additive" in this more general sense. In particular, we
show that all operator convex functions are additive for the Werner-Holevo
channel in 3x3 dimensions, which contains the well-known additivity results for
this channel as special cases.Comment: 9 pages, 1 figure. Published versio
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